Question 17

2x/(4x² + x) simplifies to 2/4x + 1

To simplify the expression 2x/(4x² + x), we can factor the denominator. The denominator can be factored as x(4x + 1), which allows us to reduce the expression to 2/(4x + 1) after canceling the common factor of x, leading to the final form of 2/4x + 1.

A) 1/x+2

This option is incorrect because it suggests that the expression simplifies to a form where x is in the denominator without properly addressing the original equation’s structure. The simplification does not yield 1/x + 2; hence, this choice does not correctly represent the simplified form.

B) 1/2x+1

Option B is incorrect as it implies a simplification that introduces a different structure than that of the original expression. The correct simplification does not lead to a fraction with 2x in the denominator; therefore, this option does not match the derived expression.

C) 2/4x+1

This option is correct. After simplifying the initial expression, we arrive at 2/(4x + 1), which is equivalent to 2/4x + 1 as it properly represents the relationship established in the simplification process.

D) 2/4x²+1

Option D is incorrect since it incorrectly suggests that the expression maintains a quadratic term in the denominator. The correct simplification does not yield 2/(4x² + 1), hence this does not accurately reflect the original expression.

Conclusion

The correct answer, C, accurately reflects the simplified form of the original expression. Other options fail to represent the proper relationship after simplification, either by introducing incorrect terms or failing to maintain the integrity of the original equation. Thus, C is the only option that correctly simplifies the expression 2x/(4x² + x).